A general fuzzy logical operator set

A general basic fuzzy logical operator set is introduced. This set reserves many properties existing in binary logic. The set consists of four abstract operators: negation, conjunction, disjunctions, and implication. The authors discuss the fact that conjunction and implication are a pair of inverse operators, which is the foundation of the general set. By using this set in approximate reasoning, rule reappearance can occur, and the detachment domain (the set in which the detachment operation a∧(a→b)=b holds) is the maximal that must be attained. Three important theorems are proved: the reasoning equivalent theorem, the condition of reproducing rule, and the maximal detachment domain theorem